Bounding the Stability and Rupture Condition of Emulsion and Foam Films

Abstract

A scaling law is presented that provides a complete solution to the equations bounding the stability and rupture of thin films. The scaling law depends on the fundamental physicochemical properties of the film and interface to calculate bounds for the critical thickness and other key film thicknesses, the relevant waveforms associated with instability and rupture, and film lifetimes. Critical thicknesses calculated from the scaling law are shown to bound the values reported in the literature for numerous emulsion and foam films. The majority of critical thickness values are between 15 to 40% lower than the upper bound critical thickness provided by the scaling law.Keywords: thin films; stability; critical thickness; spontaneous rupture; scaling law. INTRODUCTIONDespite decades of experimental (Ivanov et al., 1970;Traykov et al., 1977;Rao et al., 1982;Radoev et al., 1983;Manev et al., 1984;Kumar et al., 2002) and theoretical (Vrij, 1966a;Sheludko, 1967;Ivanov et al., 1970;Radoev et al., 1983;Sharma and Ruckenstein, 1987) investigation into the stability and rupture of thin films, very little has been published on their scaling behaviour. Thin liquid films form between the dispersed phase in emulsions and foams and become unstable when long range van der Waals forces induce the growth of capillary waves on the film interfaces (Vrij, 1966a). Upon reaching a critical thickness, films either rupture or shift to a uniform thickness and form a black film (Manev et al., 1974). Vrij (1966a, b) derived limiting equations for the critical thickness under conditions where either the Plateau border pressure drop or disjoining pressure control film drainage. Many films drain under conditions that fit into the intermediate region where both pressure terms are significant and the limiting equations are not applicable. Vrij's unique theoretical approach forced the critical thickness predictions to lower values by applying a wave-averaged corrugation growth rate expression and by specifying the rupture thickness from the film drainage curve at the minimum lifetime. The lower critical thickness predictions were still much larger than the experimental values on aniline and aqueous foam films. In this case, the overprediction was exacerbated by application of Reynolds equation and unusually large Hamacker constants. Vrij used 7 Â 10 219 J for aniline and 10 219 J for aqueous films, when the non-retarded Hamacker constant predicted from Lifshitz theory is 6.5 Â 10 220 J and 3.6 Â 10 220 J, respectively (Coons et al., 2005b). Vrij also included an undefined parameter ( f), which was inexplicably set to 6.5 and 7 for the validation films. While application of Vrij's limiting equations has the advantage of being relatively simple, frequent discrepancy with experimental results reduce their overall appeal. Ivanov et al. (1970) applied the same corrugation growth rate expressions as Vrij, but based the critical condition upon the first waveform to reach the centre of the film. This rupture criterion increases the critical film thickness...

A Review on Foam Stabilizers for Enhanced Oil Recovery

“…Some have reported that a high salt concentration reduces the electrostatic repulsion between the surfactant molecules, which facilitates the adsorption of surfactant molecules on the film. This adsorption of surfactant molecules in the presence of salt makes the lamellae rigid, and as a result the film thinning rate reduces . Filippov et al investigated the effect of chloride salts of sodium, magnesium, and calcium on bubble coalescence and bubble size.…”

“…This adsorption of surfactant molecules in the presence of salt makes the lamellae rigid, and as a result the film thinning rate reduces. 47 Filippov et al investigated the effect of chloride salts of sodium, magnesium, and calcium on bubble coalescence and bubble size. They reported that the increase in bubble size with time increases hydrodynamic stresses in the film and eventually causes turbulence with rupture as a result.…”

Rupture of Draining Foam Films Due to Random Pressure Fluctuations

“…For unstable films, the stability analysis indicates the existence of a transition film thickness at which the perturbation grows . Consequently, the critical thickness of film rupture is the film thickness at which the amplitude of imposed perturbation of optimum wavenumber (of maximum growth rate) becomes equal to one-half the film thickness. , The effect of local variations in film thickness on critical thickness is discussed, and scaling laws in terms of physical properties of the film have been proposed. , According to the conventional stability analysis, a draining foam film stabilized by repulsive interactions (electrostatic and/or steric) is always stable to an imposed disturbance since the film thickness always lies on the branch of disjoining pressure curve for which the disjoining pressure gradient is negative and therefore cannot fully explain instability in such systems. In real systems, the foam is usually exposed to random mechanical perturbations, and therefore the film may be subjected to a series of perturbations of different amplitudes and frequencies at different times.…”